I have an issue with the DNS on the wired network connection even when I have everything in auto, the DNS behaves as if it was manually set. I have deleted the network connection, and in the new one the problem persists. I have booted from a usb using the same OS and it works as expected, so it's not hardware nor the router. The DNS is set to 192.168.1.158, 8.8.8.8, 8.8.4.4

Im not sure from your post what your problem actually is. Could you be a bit more specific?

Are you trying to manually use different DNS servers than what your ISP has? If thats the case, Set them in Network Manager. What desktop are you using? Bit more info would be helpful and then I can help you.

When you are having this issue, Issue the following command to show your DNS settings. Copy the output to your next post :

I have an issue with the DNS on the wired network connection even when I have everything in auto, the DNS behaves as if it was manually set. I have deleted the network connection, and in the new one the problem persists.

Deleted them ... where?
/etc/resolv.conf says "DO NOT EDIT THIS FILE BY HAND -- YOUR CHANGES WILL BE OVERWRITTEN"

I was doing the opposite - trying to set them manually and getting the automatic stuff, so...

It appears you are not getting your DNS info from the router. Some routers if you have issues getting an I.P address then your network card will default to a private address one. To see which is the case can you connect to the internet and then in a term window run a ping test:

ping 8.8.8.8

If you get replies then your problem is only related to DNS settings and might actually be an issue with the router. You can manually go into network manager (right click panel applet for network and choose edit connections. Edit the IPV4 and see if you can enter your own DNS entries. Use 8.8.8.8 and 1.1.1.1 . If you do not use IPV6 you can go in and disable that.

It means that those are in use:
192.168.1.158
8.8.8.8
8.8.4.4
You set those in your router?
If yes, then i would think it works as intended.

dhclient will apply the settings provided by your router.
The DNS servers provided are then used by dnsmasq, which acts as a proxy.
That`s why you see 127.0.1.1 in resolv.conf as that is where dnsmasq listens.
You can check that with